Next day, heat indoor or outdoor grill to medium. In 4-quart saucepan, heat 3 inches water to boiling over high heat. Reduce heat to medium; with tongs dip romaine leaves, one at a time, into boiling water for 10 seconds to blanch. Place blanched romaine leaves between paper towels to dry.

On work surface, spread out one romaine leaf, vein side up with stem toward you. Place 1 piece mozzarella in center of leaf; top with 2 basil leaves. Fold the sides and stem end of the leaf over mozzarella and roll up leaf away from you to enclose mozzarella. Repeat with remaining romaine, mozzarella, and basil. Reserve marinade.